Does "parallel construction" mean "finding plausible but fake explanations for how we got the evidence so we don't burn our successful and secret investigation techniques"?
Just guessing from context...
The other spin would be "we discovered illegal activity through evidence that would be inadmissible in court, so we went ahead and focussed on gathering admissible evidence". Probably by looking in places they wouldn't have looked otherwise, but not by making anything up or breaking any laws.